Hey, I just added the blurb about calculating the F-test statistic. I don't have my textbook handy or I'd have noted what conditions needed to apply for this particular technique to be usable. I'm not entirely happy with the layout, so hopefully somebody else will nudge the fraction around until things look nicer. - David A. Spitzley, 12/1/04 10:52 am EST

Yeah, working through an example is great, but I'm not sure why all the calculations are needed. In particular calculating the column means (\overline{Y}) leads me into being very confused about calculating [Y] since they were the only previous Y's. Clearly I wasn't paying enough attention to the overline, but then I don't see why
they are needed at all; \overline{Y}_T also seems unnecessary. Please correct me if I'm wrong.

I also added a few sentences near the beginning in response to the many requests for simpler explanation. I hope they help a bit, and more importantly, are accurate. Regrettably, they also rely on the "factor-group" assumption, which Melcombe has already criticized (below in "Improvement required"). Does this need to be generalized, or is the categorical assumption correct for anovas? Obviously, my own understanding is still not strong enough here.

Also, perhaps these lines are too redundant with other attempts at simple clarity further below. Probably be nice to combine and get into the best spot, but trying to keep my modifications minimal given my own amateurness.

... since F-tests are used when there are no obvious "groups". Melcombe (talk) 09:24, 10 April 2008 (UTC)

This sentence is totally unclear:

"The value of the test statistic used in an F-test consists of the ratio two different estimates of quantities which are the same according to the null hypothesis being tested" —Preceding unsigned comment added by 128.40.231.243 (talk) 11:59, 21 April 2009 (UTC)

I had the chance to look up the general formuela again I'd stand by it for two reasons:1) SPSS output uses this notation for one way ANOVA 2) I looked this up in my stats book from college and it is was as I remembered it.
143.109.134.157 (talk) 04:23, 22 April 2008 (UTC)

I am very disapointed by this article for one reason: I run my regression and I got the F statistics equal to 1500 and probability F staticist equal to 0. So I came here to wikipedia to find out, if that is good or bad sign. But all I can find here is some blah blah about F distribution, normal distribution, and so on. I agree this is important, but still not very helpful for someone whith little knowledge in statistics.

PLEASE: CAN SOMEONE WHO KNOWS; ADD A SIMPLE PARAGRAPH TO THE ARTICLE ABOUT HOW THOSE F STAT SHOULD LOOOK LIKE AND WHEN IT IS A GOOD SIGN AND WHEN IT IS A BAD SIGN?

(this article is like manual to how to drive a car, that instead of explaining how to drive the car, explains how the engine is constracted)

The F-test for equality of variances is now characterized as being "extremely sensitive to non-normality". I'm generally opposed to such characterizations as it is hard for a casual reader to judge what "extreme" means. It could easily be misinterpreted as meaning something stronger than is actually warranted. But I don't have any direct experience with this rather obscure F-test (which is not the much more familiar ANOVA F-test). Skbkekas (talk) 04:55, 16 December 2010 (UTC)

"In order for the statistic to follow the F-distribution under the null hypothesis, the sums of squares should be statistically independent, and each should follow a scaled chi-squared distribution. The latter condition is guaranteed if the data values are independent and normally distributed with a common variance."

That statement is incorrect in that generality. Normality and common variance guarantee the chi-squared distribution if and only if the model either had no free parameters at all or the model is purely linear. If the model has nonlinear parameters that have been fitted by least squares, then the chi-square distribution does not apply anymore. (You can easily construct nonlinear models with 3 free parameters that can fit any data set perfectly, i.e., it produces a chi-square of zero always and its chi-square distribution is a Dirac delta function centred at zero.) In fact, the F distribution requires knowledge about the degrees of freedom. However, if nonlinear models are fit to data, the common concept of "degrees of freedom" breaks down. (If you interpret DOFs as being defined by the free parameter in the chi-square distribution, this break-down is obvious as the chi-square distribution does not apply to nonlinear models.)
That restriction to linear models only should also be mentioned in the text, alongside the restriction to nested models. It is very important to explicitly name the limitations of applicability. Otherwise, people will use the F test in inappropriate situations producing results (and maybe publishing them in scientific journals) that are not trustworthy.
-- R. Andrae, 10:49, 21 August 2011 (CEST) — Preceding unsigned comment added by 87.160.192.246 (talk)

I think the 1-rss2 in the denominator of the test statistic doesn't make sense becuase it can produce negative values. I think it should be simply rss2. — Preceding unsigned comment added by 68.149.167.250 (talk) 16:05, 2 September 2011 (UTC)

Agreed. The "1-" was added on 31 August by an IP editor. I've just undone that edit. Qwfp (talk) 07:48, 3 September 2011 (UTC)

At the end of the section on one-way anova in the "post-hoc" analysis, it is not clear where the standard error formula comes from; should it not be something like: (1−313)2+(4−313)2+(5−313)223=1.2{\displaystyle {\sqrt {\frac {\frac {(1-3{\frac {1}{3}})^{2}+(4-3{\frac {1}{3}})^{2}+(5-3{\frac {1}{3}})^{2}}{2}}{3}}}=1.2} (where 313{\displaystyle 3{\frac {1}{3}}} is the mean)? — Preceding unsigned comment added by 93.172.96.24 (talk) 15:33, 21 September 2011 (UTC)

The Formula for the F-test in the regression section was incoherent with the degrees of freedom used for the F-test after the formula.
Could someone with a statistics backgroud check the validity of the fomula in its current state?
79.60.157.114 (talk) 03:47, 7 March 2018 (UTC)